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Structure of the cubic ( or Zr) unit cell, with being the lattice constant. White and dark circles represent O and M atoms, respectively. M atoms are at the face center sites of an external cube and O atoms at the simple cubic sites of an internal cube.
Phonon spectra along the direction for cubic (solid circles) and cubic (solid triangles), with ( or Zr).
The phononic band structure of a multilayer stack, with , calculated using first-principles DFT (solid circles) and by solving the acoustic wave equation [Eq. (2)] in the continuum limit using parameters obtained from first-principles calculations (solid line).
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